A Curvature Estimation for Pen Input Segmentation in Sketch-based Modeling

Summary:

Kim and Kim propose a new corner detection system that utilizes local changes around corners.

The system starts by resampling the points of the stroke so that all points within the stroke are equidistant from one another. The curvature value at a point is typically set to equal the distance around the point divided by the changes over stroke length. By having a constant stroke distance, the system allows the direction values (calculated the same as in Sezgin and Yu) to equal the curvature values.

The final curvature value around each point is determined by two new metrics: local convexity and local monotonicity. Local convexity measures the "support" for a potential corner point. This value is calculated by looking at a window around the point and adding all of the curvature points of the same sign as the point's curvature. Local monotonicity examines the same window of points around a possible corner, but this time each point is examined in sequence, starting from the center. The curvature value can only be added if it is less than the previous point's and the same sign; if these two requirements are not met the algorithm stops and returns the current curvature.

The algorithm found the correct corners approximately 95% of the time.


Discussion:

Proposing two new (seemingly easy to implement) curvature metrics could provide corner finders with more techniques to solidify between good corners and noisy data. The paper was only published recently so I'm not sure how much of an impact it has caused yet.

The main issue I would have liked discussed more in the paper would have been where this corner finder differed from others in results. I know what types of shapes Sezgin's corner finder does well with (polylines, simple arcs) but I have yet to seen a corner finder that can continually find distinguish truly tough corners, such as a smooth line-arc transition. Kim & Kim's paper even doesn't count this transition as a corner (see Fig. 14, shapes 13 and 20). Their paper even vaguely states their accuracy rating as being "about 95 percent." I would think that if the curvature calculations were significantly better than previous corner finders' that the authors would want to show more proof. I guess we'll see how well the new metrics work this weekend...